This talk reviews recent results concerning the inviscid limit for the 2D Euler equations with unbounded vorticity. In particular, by using techniques from the theory of transport equation with no smooth vector fields, we show that the solutions obtained in the vanishing viscosity limit satisfy a representation formula in terms of the flow of the velocity and that the strong convergence of the vorticity holds and we give a rate of convergence. The talk is based on results obtained in collaboration with Gianluca Crippa (Univ. Basel) and Gennaro Ciampa (Università Milano Statale).
Stefano Spirito has been an Associate Professor in Mathematical Analysis at the University of L'Aquila since December 2021. From December 2018 to December 2021, he has been an Assistant Professor on the tenure track. He obtained a Ph.D. in Mathematics at the University of L'Aquila in 2012. After the Ph.D., he was a Post-Doc at the University of Basel and then at GSSI - Gran Sasso Science Institute. He mainly works on fluid dynamics, compressible and incompressible fluids, and linear transport and continuity equations with irregular vector fields.